# Sphaerica 7.ΠΡΟΤΑΣΙΣ ζ′. ΘΕΩΡ.-2

Theodosius of Bithynia, Sphaerica, ΒΙΒΛΙΟΝ ΔΕΥΤΕΡΟΝ., Chapter 7. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theodosius-of-bithynia/sphaerica/7.%CE%A0%CE%A1%CE%9F%CE%A4%CE%91%CE%A3%CE%99%CE%A3%20%CE%B6%E2%80%B2.%20%CE%98%CE%95%CE%A9%CE%A1.-2

Ἐὰν ὦσιν ἐν σφαίρᾳ δύο ἴσοι τε καὶ παράλληλοι κύκλοι, ὁ τοῦ ἑνὸς αὐτῶν μέγιστος κύκλος ἐφαπτόμενος ἐφάψεται καὶ τοῦ ἑτέρου. Ἔστωσαν ἐν σφαίρᾳ δύο ἴσοι τε καὶ παράλληλοι κύκλοι οἱ ΑΒ, ΓΔ· λέγω, ὅτι ὁ τοῦ ΑΒ μέγιστος κύκλος ἐφαπτόμενος ἐφάψεται καὶ τοῦ ΓΔ. Εἰ γὰρ δυνατὸν, ἐφαπτέσθω μὲν τοῦ ΑΒ μέγιστος κύκλος ὁ ΑΕ κατὰ τὸ Α σημεῖον, τοῦ δὲ ΓΔ μὴ ἐφαπτέσθω. Καὶ ἐπεὶ ἐν σφαίρᾳ μέγιστος κύκλος ὁ ΑΕ κύκλου τινὸς τῶν ἐν τῇ σφαίρᾳ τοῦ ΑΒ ἐφάπτεται, ἐφάψεται ἄρα καὶ ἑτέρου ἴσου τε καὶ παραλλήλου τῷ ΑΒ· ἐφαπτέσθω οὖν τοῦ ΕΖ. Ἐπεὶ οὖν ὁ ΑΒ τῷ ΕΖ ἴσος ἐστὶ καὶ παράλληλος, ἀλλὰ ὁ ΑΒ καὶ τῷ ΓΔ ἴσος ἐστὶ καὶ παράλληλος· καὶ ὁ ΓΔ ἄρα τῷ ΕΖ ἴσος ἐστὶ καὶ παράλληλος. Ἔσονται ἄρα ἐν σφαίρᾳ τρεῖς κύκλοι ἴσοι τε καὶ παράλληλοι, ὅπερ ἐστὶν ἀδύνατον. Οὐκ ἄρα ὁ τοῦ ΑΒ μέγιστος κύκλος ἐφαπτόμενος οὐκ ἐφάψεται καὶ τοῦ ΓΔ, ἐφάψεται ἄρα.

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Theodosius of Bithynia, Sphaerica, ed. Ernst Nizze. Text: The Greek Library, from the Perseus Digital Library and other open sources, CC BY-SA 4.0. Changes: apostrophes normalised and the text divided into reading sections by Interlinea.
License: CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Source: https://thegreeklibrary.pages.lisn.upsaclay.fr/works/tlg1719.tlg001.local001/.